Stability of the anabatic Prandtl slope flow in a stably stratified medium

Xiao, Cheng‐Nian; Şenocak, İnanç

doi:10.1017/jfm.2019.981

Cited by 6 publications

(11 citation statements)

References 57 publications

(90 reference statements)

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“…The simultaneous presence of both features makes an analytical treatment very challenging and, to the best of our knowledge, is absent in the published literature. As discovered in our earlier works (Xiao & Senocak 2019, 2020b, the primary roll instability of Prandtl's base flow consists of a pair of two counter-rotating vortices, hence any subharmonic secondary instability must involve at least two such pairs and four vortices in total, which is larger than the typical number of vortices (1 or 2) in base flow configurations that have been investigated in the current literature on stability analysis. Similar to the approach that we have pursued in Xiao & Senocak (2019), we apply linear bi-global stability analysis to identify the different modes that can destabilize the base flow vortices.…”

Section: Introductionmentioning

confidence: 90%

“…The 1-D laminar Prandtl flow profile is susceptible to multiple types of linear instabilities when the surface buoyancy flux magnitude relative to the ambient stratification is sufficiently large, as characterized by the dimensionless number (cf. Xiao & Senocak 2020 b ). As shown in Xiao & Senocak (2020 b ), at shallow slopes such as , the most dominant linear instability is a stationary mode leading to longitudinal vortices aligned along the streamwise direction within the main up-slope flow.…”

Section: Properties Of Speaker-wire Vorticesmentioning

confidence: 99%

“…Xiao & Senocak 2020 b ). As shown in Xiao & Senocak (2020 b ), at shallow slopes such as , the most dominant linear instability is a stationary mode leading to longitudinal vortices aligned along the streamwise direction within the main up-slope flow. For each , there exists an optimal wavelength that decreases with increasing where the instability attains its maximal growth rate.…”

Section: Properties Of Speaker-wire Vorticesmentioning

confidence: 99%

“…The 2-D version of the slope flow equations (2.1)–(2.3) where the along-slope direction is ignored, with imposed buoyancy flux at the no-slip bottom surface, can be solved via any time-stepping method to arrive at the steady vortices that arise as a saturated linear instability for slope angles less than when is sufficiently large (Xiao & Senocak 2020 b ). To reproduce conditions of the local linear stability analysis presented in Xiao & Senocak (2020 b ), the initial flow field is set to be the laminar Prandtl flow profile superposed with a weak sinusoidal disturbance varying along the transverse direction. The evolution of the flow field is tracked until a quasi-steady state is reached, which produces stationary vortex structures as a result of nonlinear saturation of the growing initial disturbance at sufficiently large value.…”

Section: Properties Of Speaker-wire Vorticesmentioning

confidence: 99%

“…In recent studies, we have investigated the linear stability of the Prandtl model for katabatic (Xiao & Senocak 2019) and anabatic (Xiao & Senocak 2020 b ) slope flows, as well as the extended version of the Prandtl model with ambient winds (Xiao & Senocak 2020 a ), and discovered the existence of a stationary roll instability at small slope angles, and a travelling wave instability at steeper slopes. These studies have also helped to establish the importance of the dimensionless stratification perturbation parameter in controlling the dynamics of stably stratified slope flows.…”

Section: Introductionmentioning

confidence: 99%

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Speaker-wire vortices in stratified anabatic Prandtl slope flows and their secondary instabilities

Xiao

Şenocak

2022

J. Fluid Mech.

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Stationary longitudinal vortical rolls emerge in katabatic and anabatic Prandtl slope flows at shallow slopes as a result of an instability when the imposed surface buoyancy flux relative to the background stratification is sufficiently large. Here, we identify the self-pairing of these longitudinal rolls as a unique flow structure. The topology of the counter-rotating vortex pair bears a striking resemblance to speaker-wires and their interaction with each other is a precursor to further destabilization and breakdown of the flow field into smaller structures. On its own, a speaker-wire vortex retains its unique topology without any vortex reconnection or breakup. For a fixed slope angle $\alpha =3^{\circ }$ and at a constant Prandtl number, we analyse the saturated state of speaker-wire vortices and perform a bi-global linear stability analysis based on their stationary state. We establish the existence of both fundamental and subharmonic secondary instabilities depending on the circulation and transverse wavelength of the base state of speaker-wire vortices. The dominance of subharmonic modes relative to the fundamental mode helps to explain the relative stability of a single vortex pair compared to the vortex dynamics in the presence of two or an even number of pairs. These instability modes are essential for the bending and merging of multiple speaker-wire vortices, which break up and lead to more dynamically unstable states, eventually paving the way for transition towards turbulence. This process is demonstrated via three-dimensional flow simulations with which we are able to track the nonlinear temporal evolution of these instabilities.

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Section: Introductionmentioning

confidence: 90%

Section: Properties Of Speaker-wire Vorticesmentioning

confidence: 99%

Section: Properties Of Speaker-wire Vorticesmentioning

confidence: 99%

Section: Properties Of Speaker-wire Vorticesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Speaker-wire vortices in stratified anabatic Prandtl slope flows and their secondary instabilities

Xiao

Şenocak

2022

J. Fluid Mech.

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Investigation of oscillations in katabatic Prandtl slope flows

Henao‐Garcia

Xiao

Şenocak

2022

Quart J Royal Meteoro Soc

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Dynamically unstable katabatic Prandtl slope flows are studied via numerical simulations and spectral analysis. Results confirm the presence of aperiodic temporal and spatial oscillations in the flow fields due to the emergence and propagation of flow instabilities. Damped en masse oscillations are observed to dominate the initial oscillatory stage of laminar katabatic slope flows. Stationary longitudinal rolls, which are dominant at shallow slopes, are observed to meander with increasing stratification perturbation parameter and the average distance between the rolls exhibits a strong dependence on slope inclination for slope angles less than 35∘$$ 3{5}^{\circ } $$. At much steeper slopes, traveling slope waves emerge and they are transported at the mean jet velocity. Both types of instability rolls coexist for certain combinations of dimensionless parameters, forming intricate structures that break into smaller eddies as the flow becomes more dynamically unstable. In the dynamically unstable nonturbulent regime, en masse oscillations are insignificant, but their normalised frequency can be used to discern the type of flow instability.

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Understanding Thermally Driven Slope Winds: Recent Advances and Open Questions

Farina,

Zardi

2023

Boundary-Layer Meteorol

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The paper reviews recent advances in our understanding about the dynamics of thermally driven winds over sloping terrain. Major progress from recent experiments, both in the field and in the laboratory, are outlined. Achievements from numerical modelling efforts, including both parameterized turbulence and large eddy simulation approaches, up to direct numerical simulations, are also reviewed. Finally, theoretical insights on the nature of turbulence in such winds are analyzed along with applications which benefit from progress in understanding of these flows. Open questions to be faced for further investigations are finally highlighted.

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Stability of the anabatic Prandtl slope flow in a stably stratified medium

Cited by 6 publications

References 57 publications

Speaker-wire vortices in stratified anabatic Prandtl slope flows and their secondary instabilities

Speaker-wire vortices in stratified anabatic Prandtl slope flows and their secondary instabilities

Investigation of oscillations in katabatic Prandtl slope flows

Understanding Thermally Driven Slope Winds: Recent Advances and Open Questions

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